PHYSICAL ORGANIC CHEMISTRY

PHYSICAL ORGANIC CHEMISTRY Yu-Tai Tao (陶雨台） Tel: (02)27898580 E-mail: [email protected] Website:http://www.sinica.edu.tw/~ytt

Textbook: “Perspective on Structure and Mechanism in Organic Chemistry” by F. A. Corroll, 1998, Brooks/Cole Publishing Company

References: 1.

“Modern Physical Organic Chemistry” by E. V. Anslyn and D. A. Dougherty, 2005, University Science Books.

Grading: One midterm (45%) one final exam (45%) and 4 quizzes (10%) homeworks

Chap.1

Review of Concepts in Organic Chemistry § Quantum number and atomic orbitals Atomic orbital wavefunctions are associated with four quantum numbers: principle q. n. (n=1,2,3), azimuthal q.n. (m= 0,1,2,3 or s,p,d,f,..magnetic q. n. (for p, -1, 0, 1; for d, -2, -1, 0, 1, 2. electron spin q. n. =1/2, -1/2.

§ Molecular dimensions Atomic radius ionic radius, ri：size of electron cloud around an ion. covalent radius, rc：half of the distance between two atoms of same element bond to each other. van der Waal radius, rvdw：the effective size of atomic cloud around a covalently bonded atoms.

Cl-

Cl2

CH3Cl

Bond length measures the distance between nucleus (or the local centers of electron density). Bond angle measures the angle between lines connecting different nucleus.

Molecular volume and surface area can be the sum of atomic volume (or group volume) and surface area. Principle of additivity (group increment)

Physical basis of additivity law: the forces between atoms in the same molecule or different molecules are very “short range”.

Theoretical determination of molecular size：depending on the boundary condition.

Boundary is a certain minimum value of electron density.

Molecular volume (1 au = 6.748e/Å3 ), 0.001au

0.02au

expt’l

CH4

25.53

19.58

17.12

C2H6

39.54

31.10

27.34

C3H8

53.64

42.76

37.57

C4H10

67.64

44.13

47.80

§ Heats of formation and reaction Heat of formation：Difference in enthalpy between the compound and starting elements in their standard states obtained indirectly from other components of known ΔHf° correct for necessary phase change (such as vaporization, sublimation) correct for ΔH at different T by heat capacity experimental measurement by calorimeter 　　m C(gr) ＋ n/2 H2 (g) 　　　CmHn 　　　　ΔH f° O To calculate the heat of formation of O

6 C(gr) ＋ 4 H2(g) ＋ O2(g)

(g)

O

(g) O

ΔHf°

O

6 CO2(g) ＋ 4 H2O(g) ΔHcomb= -735.9 Kcal/mol

＋ 7 O2(g)

(s) O

6 C(gr) ＋ 6 O2(g)

6 CO2(g) ΔHcomb= -94.05 (Kcal/mol C) × 6

4 H2(g) ＋ O2(g)

4 H2O(g) ΔHcomb= -68.32 (Kcal/mol H2)

O

O

(s) O

(g)

ΔHsubl= 21.46 Kcal/mol

O

ΔHf°= 6 × (-94.05) ＋ 4 × (-68.32) ＋735.9 ＋21.46 = -80.22 (Kcal/mol)

Relative difference in heat of formation O OCCF3

+ CF3COOH　　　　　　　　　∆H= -10.93 Kcal/mol O OCCF3

+ CF3COOH　　　　　　　　　∆H= -9.11 Kcal/mol ∆H= -1.82 Kcal/mol

H2

CH3CH＝CHCH3 cis H2 CH3CH＝CHCH3 trans

CH3CH2CH2CH3 ΔH=-28.6Kcal/mol CH3CH2CH2CH3 ΔH=-27.6Kcal/mol

The heat of hydrogenation is much smaller than the heat of combustion. Both will give the difference of the stability of the two isomers.

§ Bond increment calculation of heat of formation Principle of additivity：The property of a large molecule can be approximated by adding the contribution of its component.

H

For butane

H H

H H

H H

H H H

(-3.83) × 10 ＋ 3× (2.73) ＝ -30.11 Kcal/mol

§ Group increment calculation of heat of formation

3 × (-10.08) ＋ 2 × (-4.95) ＋ 1 × (-1.90) ＝ -42.04 Kcal/mol (obs. -41.66) CH3

CH3

CH3

CH3

4 × (-10.08) ＋ 2 × (-1.90) ＝ -44.12 Kcal/mol (obs. -42.49)

Further refinements correct for van der Waal strain, angle strain….

The electrostatic model for the stability of branched alkane +1 +1 +1 +1

H H H H -2

-2

H H H +1 +1 +1

-2

-2

H +1

+1

H -2

+1

H

+1

H

-3 -1 -2

H H H H +1

+1 +1

+1

H +1

Charge on H：0.278× 10-10 esu Charge on C：neutralizing charge Branched more stable JACS 1975, 97, 704.

Homolytic & Heterolytic Dissociation Energies A－B(g)

homolysis

heterolysis

ΔH°hom ：standard homolytic bond dissociation A． (g) ＋B． (g) energy electron transfer

A+ (g)＋B- (g) ΔH°het：standard heterolytic bond dissociation energy

In gas phase：ΔH°het >ΔH°hom In solution： solvation of ions can lower ΔH°het, so that heterolysis becomes favorable. Use bond dissociation energy to calculate reaction ΔH°r e.g.

CH3－H

CH3． ＋ H．

ΔH°r＝ +104 Kcal/mol

Cl－Cl

Cl． ＋ Cl．

ΔH°r＝ +58 Kcal/mol

Cl． ＋ CH3．

＋） Cl． ＋ H．

CH3Cl H－Cl

CH3－H ＋ Cl－Cl

ΔH°r＝ -84 Kcal/mol ΔH°r＝ -103 Kcal/mol

CH3Cl ＋ HCl ΔH°r＝ -25 Kcal

Hess Law：The difference in enthalpy between products and reactants is independent of the path of the reaction. by heat of formation ΔH°r＝ΣΔH°f(prd) －ΣΔH°f(pre) = -23.7 Kcal/mol at 300℃

§ Bond length and bond energy Bond length is nearly a constant property between molecules.

§ Polarizability The ability of electron cloud to distort in response to external field, defined as the magnitude of dipole induced by one unit of field gradient.

¾Polarizability decreases across a row of the periodic table, . (C>N>O>F, CH4>NH3>H2O) ¾ Polarizability increases along a column,(S>O, P>M, H2S>H2O) C-I bond is more polarizable than C-Cl ¾alkanes are more polarizable than alkenes, may due to Electronegativity. sp2 carbons are more electronegative than sp3 carbons.

§ Bonding Model Valence Bond Theory (VB) G.N. Lewis 1916 Chemical bonds result from the sharing of electron pairs between two approaching atoms. The bond is localized. + H

H

H－H H：H

The region is orbital.

Cl

+

Cl

Cl

Cl

H

+

Cl

H

Cl

σ bond from S and P

means two bonding electrons in the region between two atom each achieve a filled shell

σ bond by P and P

σ ：cylindrical symmetry For complex molecules, hybridization and resonance are used to describe molecules in terms of orbitals which are mainly localized between two atoms.

Hybridization Theory： For carbon 1s22s22p2 the 2s, 2px, 2py, 2pz hybridize to form four equivalent sp3 4 bonds can be formed on carbon highly directional sp3 orbital provide for more efficient overlap. + 3 4 methane CH4 s

sp3

p

H

H H

C

109.5°

H H

H

H H

H H

π bond, plane sym. H s + 2p → 3sp2 one p remaining H

H

or

H

H

ethene 1 2 0°

C

H

acetylene H

or

H

H-C-C

H

H

s + p → 2sp two p remaining

linear

No. of ligand

Hybri d

4

sp3

3

sp2

Trigonal

2

sp

linear

Geometry Tetrahedr CH4, CCl4, CH3OH, al CH2=CH2, H2C=O, C6H6, CO3=, CH3． HC≡CH, CO2, HCN, H2C=C=CH2

Resonance Theory： An extension of valence bond theory for molecules that more than one Lewis structure can be written. Useful in describing electron delocalization, in conjugate system and reactive intermediates. (a)If more than one Lewis structure can be written, which has nuclear positions constant, but differ in assignment of electrons, the molecule is described by a combination of these structure (a hybrid of all). (b)The most favorable (lowest energy) resonance structure makes the greatest contribution to the true structure. determining energy ： maximum number of covalent bond, minimum separation of unlike charge, placement of negative charge on most electronegative atom (vice versa). (c)Those with delocalized electrons are usually more stable than single localized structure. H 2C

C

CH

H 3C

C

C

C

C H

CH

H 3C

H

H H

H 2C 2

H

H

H H

H 2C 2

H

C

major

H

O

H

the allyl cation is planar for maximum p interaction restricted rotation around single bond

H

H C

C

C

O

more stable

H C

C

H

H H

H H

C

H 3C

two equivalent structure charge located equally on two C’s

C

C H

H 2C

O

H 3C

H

H C

C

H

significant

O

H H

C C

C

minor

H

O

§ Dipole moment：the vector quantity that measures the separation of charges.

0.1 e

+q

0.1e

-q

1 electron charge = 4.8x10-10 esu -8

d = 1.5x10 cm 0.1× (4.8× 10-10esu)

× 1.5× 10-8 cm bond dipole = q × d = = 0.72× 10-18esu．cm = 0.72 D (1 Debye = 10-18esu．Cm) Molecular dipole is the vector sum of various “bond dipoles”. It provides information about molecular structure and bonding. e.g. CH3F μ= 1.81 D H H

C H

-18 1.81× 10 q= = 0.27 e1.385× 4.8× 10-10

F

1.385Å

Cl

μ= 1.61 D

For dichlorobenzene μ= 2.30, 1.55, 0 Cl

Cl

Cl

Cl Cl Cl

From trigonometry, the calculated angles between two bond “dipole moment” are 89° , 122° , 180°. support the concept that benzene is planar. The dipole moment results from unequal sharing of the electron. due to different attraction for electron electronegativity Polar bond = [covalent bond] +λ [ionic bond] λ= weighing factor % ionic character = HCl +0.17 electron charge on H． - 0.17 electron charge on Cl． λ

λ2 × 100 % (1 +λ2)

= 0.45

§ Electronegativity & Bond Polarity Electronegativity：The power of an atom in a molecule to attract electrons to itself. Pauline 1932 χp：based on the difference in bond energy of AB and A-A + B-B other scale of electronegativity, 2 more related to atomic properties. Mulliken χ = I + A I：ionization potential of atom M 2 1934 A：e- affinity of atom Allen 1989

χspec：based on the average I.P.of all of the valence P and S electrons.

Nagle 1990

χα：based on atomic polarizability

Benson 1988

VX：no. of valence electron /covalent radii

Third Dimension of Periodic Table

J. Am. Chem. Soc. 1989, 111, 9004.

In complex molecules with many polar bonds involved, electrostatic potential surfaces (from quantum mechanic calculation) are used to view the charge distribution in the whole molecule. red ----negative potential blue --- positive potential green---neutral

-0.24 δ

-0.17 δ

δ 0.09

δ 0.36

δ F

Molecular Orbital Method Electrons are distributed among a set of molecular orbitals of discrete energies. The orbitals extend over the entire molecule. First Approximation： the MO is a linear combination of contributing atomic orb. Ψ = c1ψ1 + c2 ψ2 + ‥‥‥ + cn ψn ψ’S are basis set c’S coefficient, reflect contribution The no. of MO’s (bonding + non-bonding +antibonding) = total no. of a.o.’s For H2, 2e-

For HHe+, 2eσ*

1s

1s

1s He 1s

σ σ’*

For CO, 10e-

π x*, π y*

2Px,2Py,2Pz 2Px,2Py,2Pz

σ’ π x, π y σ’*

2s

2s

C

σ

O

MO for methane First approach ψsp31 ＝ 1 (C2s ＋ C2px ＋ C2py ＋ C2pz )

2 ψsp32 ＝ 1 (C2s ＋ C2p － C2p － C2p ) x y z 2

ψsp3 ＝ 1 (C2s － C2p ＋ C2p － C2p ) 3

x y z 2 ψsp34 ＝ 1 (C2s － C2p － C2p ＋ C2p ) x y z 2

each sp3 overlap with a 1s of H to form CH4 bond angle 109.5°

each of these has a shape of , pointing to the corner of a tetrahedron

This implies identical bonds for the bonding electrons. But ESCA data of methane shows 1s

290eV

23.0eV

12.7eV

The M.O. formed above is symmetry incorrect.

The symmetry of the M.O. must conform to the symmetry of the molecule in such a way that the M.O.’s are either symmetric or antisymmetric to all the symmetry elements of the molecule. Solution：form the delocalized methane M.O. directly form unhybridized orbitals：1C2s, 3C2p’s, 4H1s ψ1 ＝ 0.545 C2s ＋ 0.272 (H1 ＋ H2 ＋ H3 ＋ H4) ψ 2 ＝ 0.545 C2px＋ 0.272 (H1 ＋ H2 － H3 － H4) ψ3 ＝ 0.545 C2p ＋ 0.272 (H1 － H2 ＋ H3 － H4) y

ψ4 ＝ 0.545 C2pz＋ 0.272 (H1 － H2 － H3 ＋ H4)

ψ2

ψ3

ψ4

ψ1 The energy of on M.O. increase with the no. of nodes in the M.O. + +

+

+

+ +

+ + ψ1

+ -

-

+ +

+

+ -

+

-

Group orbitals from qualitative molecular orbital theory(QMOT) planar methyl

pyramidal methyl

Walsh diagram

Building larger molecule from group orbitals

Valence Shell Electron Pair Repulsion Theory (VSEPR) In predicting the shape of molecules, bonds are treated as repulsive points and the repulsive points made as far apart as possible. － counting the number of electron groups：unshared pair is a group, each bond is a group, whether single or multiple. － 2 groups

linear

3 groups

trigonal

4 groups

tetrahedral

－ non-bonding electron pair

more repulsive

－ bonding pair to electronegative groups H H

H

H C

H 109.5°

H

H

C H

∠H-C-H =109.5°

H

C H

∠H-C-H = 109.3°

N H

H

H

H

Cl 1.09Å

H

predicted ∠H-C-H = 109.5° 　　　　 ∠H-C-Cl = 109.5°

H

∠H-N-H = 107° ∠H-O-H = 104.5°

1.781Å

1.76Å

C

O H

Cl H

less repulsive

H

C H

1.096Å

H

∠H-C-H = 110°52' ∠H-C-Cl = 108°0'

Bonding electron polarized toward Cl,

Effect of lone pair on bond angle Repulsion：lone pair occupies larger domain lone pair：lone pair＞lone pair：bond pair＞bond pair：bond pair 120.2° > 109.5°

F

P

F

F

96.9° < 109.5°

Effect of lone pair on bond length The closer and larger domain of lone pair prevents a bonding pair getting closer. The adjacent bond longer F

1.79Å

F

1.68Å

F Br

F

F

Effect of electronegativity on bond angle PX3

∠XPX(° )

OSX2

∠XSX(° )

PF3

97.8

OSF2

92.3

PCl3

100.3

OSCl2

96.2

PBr3

101.0

OSBr2

98.2

Increasing electronegativity, the bonding pair shifts further away from the central atom. angle decreases Multiple bond

domain

≣ > ＝ > － O

122°

O

O S

O S

109°

H3CO 98° OCH3

Multi-center bond

H

H B

122°

H

97° B

H H

122°

H

＞

O

O S

＞O

O S

Multi-center bond occupies less domain than a single bond

Trigonal bipyramidal molecules 5 points are non-equivalent (1) the axial bond is longer than eq. bond rax/req = 1~1.4 (2) larger domain electron pair (lone pair, multiple bond) occupies equatorial position (3) more electronegative atom occupies axial position

√3 r

90° 120° √2 r

eg. PF3Cl2, PF2Cl3

PCl5 F

1.01

Cl

1.2

O

Cl

S F

F F

F

Cl

1.05

F

S

P

Cl

F

0.96

F

Cl

0.91

F

0.9

F O

O

Kr

Xe O F

F

F

F F

Cl

P

Cl

P

F F

Cl

Cl Cl

Cl

P

Cl F

F

F F

P Cl

Cl F

Cl

Limitations： － not applicable to ionic comp’d － for localized bonding/non-bonding pair, not for delocalized － for sufficiently large ligands, steric interaction prevails

§ Variable Hybridization and Molecular Geometry For carbon bonded to different atom, different hybridizations are proposed. For CH4, CCl4：sp3 hybridization % S = 25 % P = 75 hybridization index

For spn, define λ 2 = n , λ：hybridization parameter 2 λ 1 %S= ,%P= (1 +λ2) (1 +λ2) 2 sum of P-fraction Σ λi 2 = n, i (1 +λi ) 1 sum of S-fraction Σ =1 i (1 +λi2)

Interorbital angle θab ,

1+ λa2 cosθaa = 0, cosθaa =

C a

θab

sp3 sp2 sp

For CA3B sp3.5 Cl b

more P

108°

sp2.86 H a

C

H

more S-character H

a

a

110.5°

1+ λa λb cosθab = 0 if a = b,

b

→ θaa = 109.5 ° → θaa = 120 ° → θaa = 180 °

-1 λa2

the S character↑ , λ↓

3sin2 θab = 2 (1- cosθaa ) from θab = 108° , θaa = 110.5 ° from θaa = 110.5° , λa2 = 2.86 ∴sp2.86 for C－H 1

from 3 ( 1 + 2.86 ) +

1 = 1, 1 +λb2

λb2 = 3.5

For CH2Cl2 1.082Å 1.772Å

Cl

H C

112°

-1 = 2.69 cos111°47 ′ ∴sp2.69 for C－Cl

λCl2 =

from 2 (

111.47°

H

Cl

1 1 )+2( 1 + 2.69 1 +λH2

λH2 = 3.37,

from cosθHH =

-1 , θHH = 107° λH2

sp3.37 for C－H ≠ 112 ° (expt’l) λHH2 = 2.67, λCl2 = 3.39,

Cl

H

)=1

θClCl = 107°

C Cl

H

the inter-orbital bond angle smaller than the inter nuclear bond angle Cl

F 108.0°

C H

106.7°

C H

H

F 108.9°

110.52°

H

C H 109.54°

H (by inter nuclear)

H H

H

bent bond

Experimental support of variable hybridization: NMR coupling constants J13C-1H:: cyclopropane 161, cyclobutane 134, cyclopentane 128, cyclohexane 124, cycloheptane 123, cyclooctane 122

H

Cyclopropane H

115 ° 1

H

H H

H

bent bond from sp3 hybridization (or variable hybridization) Sp3.94

H

sp2.36

Walsh orbital： from sp2 hybridization

H

θcc=105°

Prediction of Physical Bonding model

Properties

with

diff.

1. Alkene Geometry C－C

ethane

ethene

ethyne

bond length

1.54Å

1.34Å

1.20Å

by σ,πformulation： sp3 hybrid. % S = 25 in ethene sp2 hybrid. % S = 33.3 S↑bond legth dec. addition π bond, shorter bond in ethyne sp hybrid. % S = 50, no quantitative prediction by bent bond formulation： 1.54Å

H

sp3

only hybridization

H

H

H

C

C

H

1.54Å

H

C

C

C－C distance

1.32Å

C－C distance

1.18Å

1.54Å

2. Acidity ethane

10-42

sp3

ethene

10-36.5

sp2

ethyne

10-25

sp

S character increase greater e--pulling power for the orbital better stabilization of the anion

bent bond formulation H

H C

H H

C

H

H

H C

C

H

C

C

H

decreased repulsion

further decrease in repulsion

conformation of propene H3C

H

H

CH2 C

H CH2

H H

H

I

I

CH2

H H

II

H

more stable by 2Kcal/mole

σ,π-formation predicts Ⅱ to be more stable, because more repulsion between double bond and the C－H bond in I Bent bond formulation： H

H H

CH2

H H

CH2 H

H

more stable

The bent bond (Ω bond ) is agreed in cyclopropane proposed or shown to more suitable than σ,π description in CF2＝CF2, CO2, CO, benzene

Conclusion